Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 8 - Rotational Motion - General Problems - Page 228: 91

Answer

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Work Step by Step

The spool rolls without slipping. It is instantaneously pivoting with respect to the point of contact with the ground. The top of the spool, compared to the center of the spool,is twice as far from the ground. Therefore, the top of the spool moves at a speed of $2v_{CM}$ relative to the ground, where $v_{CM}$ is the speed of the center of mass. This is the same as the speed of the rope, which is the same as the speed of the person, since the person is holding the rope. Therefore the person also walks at a speed of $2v_{CM}$. As the person moves forward a distance $\mathcal{l}$, the spool’s center moves a distance $\frac{\mathcal{l}}{2}$. The rope, because it is connected to the person and to the spool, unwinds by an amount $\frac{\mathcal{l}}{2}$ too.
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